Why a candidate is not a verdict
LR44, SR44W, SR44SW and PR44 can share an 11.6 × 5.4 mm envelope while using alkaline, silver-oxide or zinc-air chemistry and different operating behaviour. Conversely, CR2032 and CR2025 share a 20 mm diameter but differ by 0.7 mm in height. Dimensions narrow the search; the complete code and electrical requirements decide the family.
Examples where both measurements matter
Several silver-oxide watch cells are 1.65 mm high but have very different diameters. Compare SR416SW / 337 at 4.8 × 1.65 mm, SR716SW / 315 at 7.9 × 1.65 mm and SR1116SW / 366 at 11.6 × 1.65 mm. A matching height cannot compensate for the wrong diameter.
After narrowing the list, read Battery voltage and chemistry before treating any candidate as a substitute.